Finite Group DatabasebetaFinite Group Databasebeta| order | 832 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C13 ⋊ #559 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D13 |
| commutator, socle, cosocle | C22×C13 | C24 |
| Fitting, prime radical | C13×#127 | C2 |
| hypercenter | #127 | D13 |
| hypocenter | C13 | #559 |
| LCS | G ▷ C22×C13 ▷ C13 | |
| UCS | C1 ◁ C22 ◁ #127 | |
236 conjugacy classes of subgroups.
| transitive degree | μt(G) = 416 |
Polycyclic presentation:
2^6,13|a^2=f,d^2=f,d^a=def,g^a=g^12,c^b=ce,d^b=df,d^c=df109 conjugacy classes — view the full character table.
| maximal subgroup of | #13113893, #13113896, #13113955, … |
| maximal normal subgroup of | #13113893, #13113896, #13113955, … |
| maximal quotient of | #13117795, #13117808, #13117901, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(832, 1384);